Surjective and closed range differentiation operator
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909651485851648 |
|---|---|
| author | Mengestie, Tesfa |
| author_facet | Mengestie, Tesfa |
| contents | We identify Fock-type spaces $\mathcal{F}_{(m,p)}$ on which the differentiation operator $D$ has closed range. We prove that $D$ has closed range only if it is surjective, and this happens if and only if
$m=1$. Moreover, since the operator is unbounded on the classical Fock spaces, we consider the modified or the weighted composition--differentiation operator, $D_{(u,ψ,n)} f= u\cdot\big( f^{(n)}\circ ψ\big)$, on these spaces and describe conditions under which the operator admits closed range, surjective, and order bounded structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Surjective and closed range differentiation operator Mengestie, Tesfa Functional Analysis We identify Fock-type spaces $\mathcal{F}_{(m,p)}$ on which the differentiation operator $D$ has closed range. We prove that $D$ has closed range only if it is surjective, and this happens if and only if $m=1$. Moreover, since the operator is unbounded on the classical Fock spaces, we consider the modified or the weighted composition--differentiation operator, $D_{(u,ψ,n)} f= u\cdot\big( f^{(n)}\circ ψ\big)$, on these spaces and describe conditions under which the operator admits closed range, surjective, and order bounded structures. |
| title | Surjective and closed range differentiation operator |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2506.14410 |